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Sommersemester 2019
10.04.2019 um 17:15 Uhr in 69/125
Prof. Dr. Christian Stump (Ruhr-Universität Bochum)
Counting Inversions and Descents of Random Elements in Finite Coxeter Groups
"Permutation statistics" (this is, assigning numbers to permutations) is a fundamental concept from Combinatorics. Among the most important are the Mahonian and Eulerian numbers given by the number of inversions and by the number of descents. in this talk I report on Mahonian and Eulerian statistics in general finite Coxeter groups by discussing properties of their probability distributions that we exhibited using the Combinatorial Statistics Database FindStat. I will provide uniform formulas for their mean values and variances in terms of Coxeter group data, and I will also discuss the double-Eulerian probability distribution given by the sum of descents and inverse descents. I will finally establish necessary and sufficient conditions for general sequences of finite Coxeter groups of increasing rank for which Mahonian and Eulerian probability distributions satisfy central and local limit theorems. This talk is based on recent collaborations with Thomas Kahle.
24.04.2019 um 17:15 Uhr in 69/125
Prof. Dr. Marcel Campen (Universität Osnabrück)
Beyond Simplicial: Advanced Discretizations of 3D Domains for Visualization and Simulation
A key component in computational applications that operate on three-dimensional domains, such as digitized real-world objects or virtually designed assets, are techniques for the discretization of these domains and of data defined over these. Goal is the representation or approximation by a finite number of compactly representable elements, enabling efficient processing using practical algorithms. Drawing from solid theoretical results, discretizations based on simplicial complexes (called triangular or tetrahedral meshes in this context) have been prevalent in practice for decades. However, non-simplicial discretizations are known to be beneficial for a variety of use cases. In this talk recent advances in the field of algorithmic generation and optimization of non-simplicial complexes for the representation and approximation of three-dimensional domains will be discussed. We will consider the case of elements which are non-simplicial combinatorially (e.g. complexes of quadrilateral or hexahedral elements) as well as the case of elements being non-simplicial geometrically (i.e. non-linear elements). We will touch upon a variety of questions and problems that still are open in this field — from a theoretical perspective (e.g. existence conditions, quality bounds) as well as a practical point of view (numerical robustness, efficiency).
02.05.2019 um 17:15 Uhr in 69/125 Achtung: Donnerstag!
Prof. Dr. Adrian Röllin (National University of Singapore)
From Berry-Esseen to Stein
Starting from the classical Berry-Esseen theorem and characteristic functions, we give a gentle introduction to Stein’s method along with recent applications to central limit theorems with dependence arising in random graph theory
15.05.2019 um 17:15 Uhr in 69/125
Prof. Dr. Matthias Köppe (University of California, Davis)
Cutgeneratingfunctionology: Infinite-dimensional Methods for Integer Linear Optimization
In the theory of valid inequalities for integer point sets in polyhedra, the traditional, finite-dimensional techniques of polyhedral combinatorics are complemented by infinite-dimensional methods, the study of cut-generating functions. I will give an introduction to these methods and will explain their connection to lattice-free convex bodies. I will present recent results involving inverse semigroups of partial maps, obtained jointly with Robert Hildebrand and Yuan Zhou.
22.05.2019 um 17:15 Uhr in 69/125
Prof. Dr. Timo de Wolff (Technische Universität Braunschweig)
An Introduction to Nonnegativity and Polynomial Optimization
In science and engineering we regularly face hard, nonlinear polynomial optimization problems.
Solving these problems is essentially equivalent to certifying nonnegativity of multivariate, real
polynomials – a key problem in real algebraic geometry since the 19th century.
In this talk, we discuss how to tackle such problems both from the perspective of algebra and
optimization.
05.06.2019 um 17:15 Uhr in 69/125
Prof. Dr. Dirk Lorenz (Technische Universität Braunschweig)
Analysis and Algorithms for Optimal Transport
How to move mass or goods from where they are to designated places in the most efficient way? This question was posed in geometrical terms by Gaspard Monge in the 18th century already. In the middle of the 20th century Leonid Kantorovich reformulated to problem in the language of measure theory and developed a solution theory (which actually earned him the Nobel prize in economics in 1975). In recent days there have been an increasing interest in the mathematics of optimal transport and computational tools have been developed which helped to make optimal transport applicable in fields like mathematical imaging, machine learning or inverse problems.
In this talk I will introduce various formulations of optimal transport problems (involving, e.g. dynamics of partial differential equations, minimization problems with static partial differential equations as constraints, linear programming, or matrix scaling). I will shortly speak about the analysis of the problems and then focus on the computational problem of developing practical algorithms.
12.06.2019 um 17:15 Uhr in 69/125
Prof. Dr. Stefanie Rach (Otto-von-Guericke-Universität Magdeburg)
Mathematiklernen in der Studieneingangsphase
Welche Bedeutung haben individuelle Lernvoraussetzungen für den Studienerfolg im ersten Semester?
Abstract: Beim Übergang vom schulischen Mathematikunterricht in ein Mathematikstudium werden Lernende mit zwei Herausforderungen konfrontiert: Zum ersten müssen Studierende mit der für sie eher unbekannten wissenschaftlichen Mathematik umgehen, zum zweiten müssen sie die präsentierten mathematischen Inhalte häufig selbstständig für ihren eigenen Lernprozess aufbereiten. Welche kognitiven und affektiv-motivationalen Lernvoraussetzungen zur Bewältigung dieser Herausforderungen sinnvoll sind, steht in diesem Vortrag im Vordergrund. Als Diskussionsgrundlage werden Ergebnisse empirischer Studien mit Fach- und gymnasialen Lehramtsstudierenden vorgestellt.
